Sap flow gauge

ABSTRACT

A sap flow gauge (10) which can accommodate stem or other plant parts (S, S&#39;) of very small and/or varying cross-sectional configuration is provided which includes a generally U-shaped body (12) presenting a central bight portion (50), a pair of spaced, opposed legs (52, 54) and a stem-receiving passageway (56). The body (12) preferably includes a pair of spaced, endmost filler pads (16, 18) which support a bridging strip-type resistance heater (28). The heater (28) has one end thereof affixed to an adjacent filler pad (16), with the remaining end of the heater (28) thereof being free. A flux sensing thermopile (40), as well as spaced, temperature differential sensing thermocouple pairs (44, 46) are also supported by the central bight region of the body (12). In practice, the gauge (10) is applied to a stem (S, S&#39;) by wrapping the body (12) around the stem (S, S&#39;) with strip heater (28) in engagement with the stem (S, S&#39;); the filler pads (16, 18), together with the free end of the strip heater (28) insure close, conforming, heat transfer engagement between the strip heater (28) and the stem (S, S&#39;) .

This application is a continuation of application Ser. No. 08/085,614,filed Jun. 30, 1993, now allowed.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is broadly concerned with an improved heat balancesap flow gauge which is especially configured to accommodate irregular,non-circular, and/or very small diameter plant stems and parts and givevalid sap flow testing results with such stems or parts. Moreparticularly, the invention is concerned with such a sap flow gaugewhich is improved by provision of a U-shaped main body carrying acentral heating element as well as radial heat flux and temperaturedifferential sensors; in preferred forms, the U-shaped body is providedwith filler means disposed between the legs of the U-shaped body forinsuring proper engagement between the plant part and the bight heatingmeans. The heating means advantageously is in the form of an elongatedresistance heater strip, with one end of the strip being secured to thebody and the other end thereof free.

2. Description of the Prior Art

Direct, accurate, non-invasive and continuous measurement and analysisof transpiration in herbaceous plants and trees has long been a goal ofagronomists. The heat balance method for measuring plant water loss hasprovided a reliable technique and has been used on a wide variety ofplant species in many diverse applications. Field studies have used sapflow gauges as a means of partitioning evapotranspiration for examiningenergy transport phenomena in agricultural settings. Other studies haveused these gauges to examine water use, the effects of growth retardantson horticultural plants in urban environments and to measure water lossin natural ecosystems.

The theoretical basis for the heat balance method is based upon thermalflow meter techniques used for measuring gas flow rates through acontained volume by applying heat over a short region and measuring theresulting temperature distribution and heat fluxes within the heatedsegment. Application of this technique to plant stems and a thoroughdiscussion of the mathematical equations are provided by: Sakuratani,Jap. Agricultural Meteorology, 37:9-17 (1981) and Baker et al., Plant,Cell and Environment, 10:777-782 (1987).

Briefly, however, the heat balance method uses energy balance conceptsto account for the heat fluxes within an insulated segment of plantstem. The energy balance of a heated plant stem can be defined as

    Q=Q.sub.v +Q.sub.r +Q.sub.f +S                             (1)

where Q represents the heat energy supplied, Q_(v) is the apical andbasal heat energy transferred by conduction along the stem axis, Q_(r)is the radial conduction of energy perpendicular to the stem axis, Q_(f)is the heat energy transported by the mass flow of water, and S is therate of change in heat storage of the stem segment, all with units ofwatts (W). convective energy flux in the sap can be defined as

    Q.sub.f =cF(T.sub.so -T.sub.si)                            (2)

where c is the specific heat of water (J/kg.K), F is the rate of waterflow in the stem (kg/s), and T_(so) -T_(si) is the temperaturedifference between the water flowing into and out of the heated segment.S is typically neglected because of the assumption of steady stateconditions in the system. By substituting eqn 2 into eqn 1, theformulation of a mass flow equation for the heated stem segment is

    F=(Q.sub.f -Q.sub.v -Q.sub.r)/(c(T.sub.so -T.sub.si))      (3)

An important variable in calculating F is the estimate of the gaugeconductance, K_(g), which is used in determining Q_(r). Values for K_(g)are found by setting F=O in eqn 3, solving for Q_(r), and dividing bythe thermopile output. Sap flow rates close to zero can be obtained fromexcised stems or by using low night-time flow rates and assuming thatsap flow is zero.

In most cases, published field studies have used large mature plantswith stems larger than 10 mm in diameter and mainly with circular stemradial geometries. One study (Sakuratani, Jap. Agricultural Meteorology,45:277-280 (1990)), investigated plants with stem diameters smaller than10 mm, but the species used had a stem with a circular radial geometry,and the gauge design employed did not allow for easy gauge placement andremoval. Large stem diameters with circular geometries allowed easyapplication of typical rigid cylindrical sap flow gauges. Stem diametersof dicot seedlings may be less than 10 mm, while many maturedomesticated monocots have stems of 5 mm or less in diameter.Furthermore, stem geometries of many dicot seedlings are not circular,and the geometries of many native monocots are highly elliptical.

One prior sap flow gauge is in the form of a cylindrical membersupporting an internal stem heater having resistance heating elementsuniformly positioned along the length thereof. The cork backing of themember is composed of three individual pieces of cork, one for theheater and thermopile, and two separate pieces for the upper and lowerthermocouple pairs. Different stem sizes are accommodated by alteringheater length and width. However, adjusting the heater length for stemdiameters near 5 mm or smaller is difficult, because the wire leadsneeded for input voltage interfere with the stem-heater interface. Also,the provision of three cork pieces makes it difficult for this priorgauge to accommodate noncircular plant stems.

There is accordingly a need in the art for an improved sap flow gaugewhich can more readily accept small and non-circular stems or plantparts, while at the same time giving accurate stem flow measurementresults.

SUMMARY OF THE INVENTION

The present invention overcomes the problems outlined above, andprovides an improved sap flow gauge in the form of a generally U-shapedbody having a central bight portion and a pair of spaced opposed legs.The bight portion presents a passageway therethrough for receiving aplant part such as a stem, with the legs extending generally laterallyfrom the plant part. The overall gauge also includes heating meansadjacent the bight and oriented for heating the plant part receivedwithin the passageway. Means is provided for sensing radial heat fluxand temperature differential values exhibited by the plant part inresponse to heating thereof by the heating means.

Preferably, filler means is disposed between the legs of the body andlocated proximal to the plant part for insuring proper engagementbetween the plant part and heating means, when the gauge is applied to aplant part. Additionally, the heating means is advantageously in theform of a elongated strip supporting a resistance heater element, withone end of the strip being secured to the body, while the other endthereof is free.

In actual practice, the U-shaped body is formed of cork-neoprene gasketmaterial and has a pair of filler pads (likewise formed of the gasketmaterial) secured to each of the inner faces of the body legs. Theradial heat flux sensing means comprises a multiple-junction thermopilecarried by the bight portion adjacent the heating means, The temperaturedifferential sensing means includes a pair of spaced thermocouplessupported on the bight on opposite sides of the thermopile.

In use, the U-shaped body is positioned about a stem or other plantpart, with the heater element engaging the plant part. A jacket ofthermal insulation material is then applied to the U-shaped body, and areleasable spring clip is affixed for releasably pressing the legs ofthe body together. This causes the filler pads to close against theheating strip and insure close engagement between the plant part andheating strip. It will also be appreciated that the attachment of theheating means with one end thereof free insures that the heater willfirmly wrap around and engage substantially all of the outer surface ofthe plant part.

Appropriate leads are secured to the heating element and sensors, andthese are in turn connected with conventional monitoring apparatus.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plan view of the primary body of the sap flow gauge of theinvention, with the strip heating element removed to illustrate theconstruction and location of the bight sensors;

FIG. 2 is a view similar to that of FIG. 1, but illustrating the stripheating element affixed to the primary body;

FIG. 3 is a side view of the body depicted in FIG. 2 and illustratingthe connection of the strip heating element;

FIG. 4 is an isometric view of the U-shaped gauge applied to a plantpart;

FIG. 5 is a sectional view further illustrating the application of thegauge to the plant part;

FIG. 6 is an isometric view similar to that of FIG. 4, but depicting useof the external insulating jacket and spring clip;

FIG. 7 is a view similar to that of FIG. 5, but illustrating applicationof the gauge to a non-circular, generally elliptical in cross-sectionplant part;

FIG. 8A is a graph depicting the performance of the gauge of theinvention (dotted line) versus results from gravimetric measurements(full line), with a soybean seedling having a stem diameter of about 3mm;

FIG. 8B is a graph depicting the heat balance components recorded duringthe soybean seedling test where Q=power input, Q_(f) =convective heatflux, Q_(r) =radial heat flux, and Q_(v) =axial heat flux;

FIG. 8C is a graph of T_(so) -T_(si) during the soybean seedling test ofFIGS. 7A-7B;

FIG. 9 is a graph of T_(so) -T_(si) in relation to sap flow rate atdifferent input power (Q) levels;

FIG. 10 is a graph illustrating change in apparent sap flow ratefollowing stem excision recorded every 1 s; and

FIG. 11 is a graph illustrating the system time constant derived fromthe difference from initial (SF) and final (SF_(final)) sap flow ratewith the latter value being 63% of the initial rate.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Turning now to the drawings, and particularly FIGS. 1-3, a sap flowgauge 10 is depicted. Broadly speaking, the gauge 10 includes a mainbody 12 having a planar substantially square (e.g., 50 mm×50 mm) primarypanel 14 carrying a pair of adhesively secured, laterally spaced apart,endmost filler pads 16, 18. In addition, the overall gauge 10 includesheating means 20 as well as means 22, 24 for sensing radial heat fluxand temperature differential values exhibited by a plant part inresponse to heating thereof.

In more detail, the main panel 14 and filler pads 16, 18 are preferablyformed of flexible neoprenecork automotive gasket material having athickness of 2 mm. As best seen in FIGS. 1 and 3, the filler pads 16, 18are secured to the end regions of the primary panel 14, to define arecessed region 26 therebetween. As best seen in FIG. 2, the filler pads16, 18 have a width which is greater than the width of the recessedregion 26 therebetween.

Heating means 20 is in the form of an elongated Kapton-film electricalresistance heater (Heater Designs, Inc., Bloomington, Calif.). Asillustrated in FIG. 2, the heating means includes a dielectric Kaptonbacking strip 28 which supports a resistance heating element 30 which issituated primarily in the region between the filler pads 16, 18. Inaddition, a pair of terminals 32, 34 are provided adjacent the opposedends of the strip 28, and appropriate wire leads 36, 38 are affixed tothese terminals. In this regard, the heating element 30 is situatedcentrally on the strip 28, and integral connector leads 30a, 30b extendfrom the ends of element 30 to the terminals 32, 34. It will be seenthat the length of each of the end regions of strip 28 are at leastequal to the length of the central resistance heater element 30. Theconnector leads 30a, 30b are of sufficient thickness relative to heatingelement 30 so that essentially no heat is generated by passage ofcurrent through the connector leads. This configuration insures that allplant part heating is generated in the central region of the stripheater. As best illustrated in FIG. 3, one end of the strip 28 isadhesively secured to filler pad 16, whereas the remaining end of thestrip 28 is free. Note also that the strip 28 is of sufficient length toeffectively bridge the distance between the pads 16, 18.

The flux sensor 22 is in the form of a thermopile 40 (10-14 junctions)constructed from 0.127 mm diameter (36 AWG, American Wire Gauge) copperand constantan wires. The thermopile wires are woven into primary panel14 as shown, in the recessed region 26 between the pads 16, 18.Appropriate thermopile electrical leads 42 extend from the rearmostsurface of panel 14 as shown.

Temperature differential sensor 24 is in the form of two pairs ofthermocouples 44 and 46 located above and below the flux sensor 22 andmounted on the inner face of primary panel 14 between the pads 16, 18.Appropriate electrical leads 48 extend from the rear surface of primarypanel 14 as shown. In the illustrated embodiment, the spacing betweenthe thermocouples and the heater, as well as between the thermocouplepairs is 3 mm.

In the use of gauge 10, the body 12 is folded about an elongated plantpart such as a stem S to achieve a generally U-shaped configuration asshown in FIGS. 4 and 5, thus presenting a central arcuate bight 50 and apair of spaced opposed legs 52, 54, as well as an open-ended passageway56. As best seen in FIG. 5, the legs 52, 54 have a length correspondingto the width of the pads 16, 18, with such length being greater than themaximum transverse dimension of passageway 56. This geometry isimportant in order to accommodate smaller diameter and non-circularstems or plant parts. Again referring to FIG. 5, the stem S is receivedwithin the passageway 56, with the strip heater 28 wrapped around asubstantial portion of the outer surface of the stem, The portions ofthe strip 28 overlying the filler pads 16, 18 are pressed into contactwith each other, with the pads thus insuring a firm contact between stemS and the central resistance heater 30 carried by the strip 28. Thisconfiguration also insures that the leads 36, 38 do not interfere withheater-plant part contact in the passageway 56.

The complete assembly for sap flow measurement is illustrated in FIG. 6.In particular, a jacket 58 of flexible foam insulating material isapplied around the U-shaped body 12, and a conventional spring clip 60is attached to hold the entire assembly in place on stem S. In thisconnection, the laterally extending legs 52, 54 and the surroundingjacket 58 provide an unobstructed gripping region for the clip 60 andprevent interference with the wire leads or the other functionalcomponents of the gauge 10.

As indicated above, the present invention can readily accommodate stemsor other plant parts of noncircular cross-section. For example, asillustrated in FIG. 7, a generally elliptical stem S' is depicted withthe gauge 10 applied thereto. In this regard, it will be seen that thestrip heater 28 can wrap about substantially the entire outer surface ofthe stem S' just as in the case of circular stem S illustrated in FIG.5. Provision of the resistance heating element 30 in the central bightregion of the body 12, together with the free, unconnected end of thestrip 28, allows the heater 28 to conform with such non-circular plantparts.

In measurement operations, the gauge 10 is applied to a plant part asillustrated, and the wire leads 36, 38 from strip heater 28 areconnected to a DC power supply. The remaining leads 42, 48 from thethermopile 40 and thermocouple pairs 44, 46 are connected with a datalogger or other conventional controller.

EXAMPLE

Several gauges of the type described above were constructed and testedon container grown Glycine Max (soybean) [(L.) Merr. var Williams 82]plants in the laboratory under two high pressure sodium lamps (LU 400,Energy Technics, York, Pa.). Tests were then performed in a greenhouseunder normal diurnal patterns of solar radiation and temperature.Voltage input to the gauge heaters was supplied with a DC power supply(Hewlett Packard 6284A, Berkeley Heights, N.J.). Gauge signals weresampled every 15 seconds with a data logger (21X, Campbell ScientificLtd., Logan, Utah) and stored as 15- or 30-minute averages. Gaugemeasurements of sap flow rates were compared with gravimetricmeasurements of water loss obtained from an electronic balance. Beforeeach test, pots were well watered, allowed to drain and sealed inplastic bags to minimize soil evaporation. During testing, the gaugeswere surrounded with insulation and shielded from radiation withaluminum foil.

FIG. 8A presents an example of results from a laboratory test on asoybean seedling having a stem diameter of 3 mm, and shows that gaugeestimates of sap flow closely tracked gravimetric measurements oftranspiration. The gauge was placed directly above the cotyledons wherestem geometry was square with a unit side length s=3 mm. Leaf area(one-sided) of the plant was approximately 0.18 m². For this particulartest, the cumulative flow estimate from the gauge (155 g) was only 2%less than the gravimetric measurement of water loss (157 g). Alllaboratory gauge estimates were consistently within ±5% of gravimetricwater losses.

Dynamic responses of the heat balance components during this testdemonstrated the comparative importance of different heat fluxes atdifferent flow rates (see FIG. 8B). During periods of low flow, Q_(r) isthe dominant flux component of the total power input (Q). During highflow, however, Q_(f) becomes the dominant flux component and therelative importance of Q_(r) diminishes. Q_(v) was consistently a minorflux component regardless of flow rate. Such relative patterns of heatflux components are consistent with prior data collected from largerstems (Steinberg et al.; Agronomy Journal, 82:51-854 (1990); Dugas,Theoretical and Applied Climatology, 42:215-221 (1990); Ham et al.,Agricultural and Forest Meteorology, 52:287-301 (1990)). However, incontrast to previous studies where T_(so) -T_(si) varied from 1.0°-7.0°C. when flow rates changed, fluctuations in T_(so) -T_(si) in this testwere minimal (0.5°-1.0° C.) with no apparent relationship to sap flow(FIG. 8C).

Another greenhouse test was performed to demonstrate the performance ofthe gauge under changing soil water regimes. The test used the same typeof plant described above, with the gauge being placed immediately abovethe cotyledons where the stem was square (s=4 mm) and left undisturbedfor a period of 5 days. Plant height was approximately 0.5 m and totalleaf area (one-sided) was 0.29 m².

Results from a greenhouse test over 5 consecutive days (4-8 Sep.)demonstrate the performance of the gauge under changing soil waterregimes (FIG. 9). For this test, the gauge was again placed immediatelyabove the cotyledons where the stem was square (s=4 mm) and leftundisturbed for the entire period. Plant height was approximately 0.5 mand total leaf area (one-sided) was 0.29 m². Clear skies predominatedwith daily total global irradiance in the greenhouse close to 5.0 MJ m⁻²d⁻¹ (pyranometer, Model 8-48, Eppley Laboratory, Newport, R.I.) and airtemperatures ranged from 19°-32° C. Soil water availability was nearsaturation at the start of the test, and no additional water wassupplied until the evening of the fourth day when the pot was again wellwatered. Gravimetric water loss reached a maximum near 50 g/h on thefirst day, steadily declined thereafter as soil water was depleted andrecovered to 30 g/h after rewatering. Based on total plant leaf area,the range of water loss rates corresponded to average transpirationalmolar fluxes of 0.5-2.7 mmol m⁻² s⁻¹.

With high soil water availability on days 1 and 5, the gauge andgravimetric measurements for both the 15-minute averages and dailytotals generally correlated well (Table). With adequate soil water, themidday absorption lag in sap flow may have been the result of hydrauliccapacitance and internal plant resistances to water flow. On subsequentdays, the sap flow estimates steadily declined until day 4 when thecumulative measured sap flow was only 55% of the gravimetric water loss.The increasing discrepancy between the two estimates could be explainedby neglect of the heat storage term (S) in the energy balance equation,errors in heat flux or temperature measurements during low flows, ordecreased plant absorption as soil water was depleted.

The following table summarizes the results of this test, and sets forthdaily total global irradiants (R_(s)), maximum and minimum airtemperatures (T_(a)), maximum stem surface temperature (T_(s)), middaysoil water content (w) and availability, minimum predawn gaugeconductance values (K_(g)) and sap flow gauge accuracy for 5 consecutiveSeptember days in a greenhouse located at Manhattan, Kans. The plant wasrewatered at the end of day 4.

                                      TABLE                                       __________________________________________________________________________    R.sub.S    T.sub.a(°C.)                                                                 T.sub.S (°C.)                                                               w   % H.sub.2 O.sup.1                                                                  K.sub.g                                        Day                                                                              (MJ m.sup.-2 d.sup.-1)                                                                Max                                                                              Min                                                                              Max  (g.sup.-1)                                                                        available                                                                          (W)                                                                              accuracy.sup.2 (%)                          __________________________________________________________________________    1  5.0.sup.3                                                                             30 19 35   0.83                                                                              131  0.625                                                                            -3.6                                        2  5.4     30 21 35   0.55                                                                               62  0.733                                                                            -7.8                                        3  5.2     30 24 37   0.38                                                                               25  0.771                                                                            -31.5                                       4  5.3     31 24 39   0.29                                                                               9   0.821                                                                            -45.5                                       5  5.1     32 26 34   0.80                                                                              113  0.811                                                                            -2.2                                        __________________________________________________________________________     .sup.1 calculated from soil water release data and the equation M.sub.w -     M.sub.wmin)/M.sub.w(-0.03MPa) -M.sub.wmin) where M.sub.w was the amount o     water (g) contained in the pot, at noon, for a particular day, M.sub.wmin     was the amount of water present at the minimum water content (g g.sup.-1)     recorded during the study, and M.sub.w(-=0.03MPa) was the amount of water     present at a soil water potential of -0.03 MPa.                               .sup.2 difference between diurnal cumulative gauge andgravimetric water       loss measurements divided by the gravimetric total.                           .sup.3 outer surface of greenhouse was coated with whitewash to reduce        irradiance penetration.   Potential sources of errors in sap flow             measurements

The rate change in heat storage is often ignored when applying the heatbalance technique. This approach has largely been accepted, particularlyfor stems of herbaceous plants where, because the small size of theheated segment and the near steady-state conditions, the magnitude ofheat storage capacities are small in relation to the other components ofthe energy balance. Over short periods of time, however, systematicerrors could theoretically be corrected to improve sap flow estimates.To determine if the effect of neglecting S was significant on days 3 and4, the estimate flow rates were recomputed using the absolute stemtemperatures measured immediately above and below the heated stemsegment. The rate change in heat storage was computed as

    S=V. C.sub.v. (ΔT/Δt)                          (4)

where V is the volume of the stem segment (,³), C_(v) is the volumetricheat capacity of the stem tissue (J/m³.K), and Δt/Δt is a finitedifference estimate of the rate change in stem temperature (K/s). Thestem segment temperature was determined by averaging the upper and lowerthermocouples closest to the heater. The volume of the segment was 126mm³, and C_(v) was held constant at 4.175 J/m³.K. Results showed thatincluding S in the stem energy balance adjusted the flow estimates byless than 1 g/d for the cumulative totals and did not noticeably alterthe diurnal patterns. Values of S ranged from -0.001 to 0.002 W over thecourse of the day and were always less than 3% of the total heat flux.Including S in the flow estimates on days 1, 2, and 5 when flows werehigher produced similar results. This is in contrast to Groot et al.,Agricultural and Forest Meteorology, 59:289-308 (1992) who speculatedthat including S in the stem energy balance improved the diurnalperformance of a sap flow gauge attached to a conifer seedling with astem diameter of 6 mm. In this study, the concurrent gravimetricmeasurements of water loss confirmed that S had no significant effect onthe flow measurements. The primary reason that S was insignificant inthe flow measurements was the small stem volume.

As in the laboratory tests results depicted in FIGS. 8A-8C, the dominantheat flux during periods of maximum flows on 1, 2, and 5 was Q_(f). Incontrast, as flow rates decreased on days 3 and 4, Q_(r) was thedominant flux even as flow rates approached the daily maximums. Thischange in the dominating flux component at maximum flow rates (Q_(F) vsQ_(r)) has implications for potential errors in sap flow estimates. Inthe flow equation, the heat fluxes Q, Q_(v), and Q_(r) and the systemT_(so) -T_(si) are obtained from direct sensor output and Q_(F) iscalculated as the residual energy flux. With Q being a constant andQ_(v) usually a minor portion of the total heat balance, Q_(r) andT_(so) -T_(si) become the most important factors in estimating sap flowrates. Furthermore, the relative importance of Q_(r) and T_(so) -T_(si)depends on the flow rate and which heat flux dominates the stem energybalance.

During periods of higher flows, when the importance of Q_(r) decreasesand Q_(f) dominates the energy flux, sap flow estimates become moresensitive to errors in T_(o) -T_(i). Sample calculations from day 1,when the highest sap flows (>50 g/h) occurred, showed that a 0.1° C.error in T_(so) -T_(si) would have caused a 15% error in F. At the sametime, a 10% error in Q_(r) would have caused only a 6% error in F. Incontrast, on day 4, when the maximum flows were much lower (6 g/h), asimilar error in T_(so) -T_(si) and Q_(r) would have resulted in a 3%and 25% error in F, respectively. Thus, at high flows, the gauge issusceptible to errors in T_(so) -T_(si), and, at low flow rates, thegauge is sensitive to errors in Q_(r). On day 4, when Q_(r) was thedominant heat flux, the large difference between the gauge andgravimetric water loss rates could have been due to errors in Q_(r).

Sap flow gauges, however, only measure water movement through the plantstem and not actual water transpired from the plant to the atmosphere.When plant water uptake is restricted by soil water availability, sapflow rates measured with a gauge may not accurately reflectgravimetrically measured water loss rates which representstranspiration. Soil water availability on days 3 and 4 had declined to25% and 9% respectively, of initial available water (Table). On day 4,plant leaves were noticeably wilted, suggesting that tissue hydrationwas not being maintained and plant water absorption was severelylimited. Thus, differences between the gravimetric and gauge estimatedwater loss on those days may simply have resulted from decreased plantwater uptake from the soil. However, a more detailed investigation,simultaneously measuring plant tissue water content or water potentialand soil water availability, would be needed to distinguish betweenplant desiccation and errors in sap flow estimates.

Gauge operation

Successfully operating sap flow gauges requires a procedure fordetermining K_(g) and the proper power input, Q. The Table results wereobtained using pre-dawn K_(g) values, when gravimetric water loss rateswere typically near 1 g/h (Table). The 30% increase in K_(g) through day4 may have been due to declining soil water availability that resultedin lower stem water content. Fluctuating stem water content would affectthe residual K_(g) estimate by altering the estimate of Q_(v) and theresultant estimate of Q_(r). Lower stem water content would meandifferent volumetric proportions of water and cellulose, which directlyaffects stem thermal properties. Decreasing water content may also causethe stem diameter to shrink and alter the thermocouple stem surfacecontact, resulting in errors in Q_(v) Either scenario would explain thesmall decrease in K_(g) on day 5 after watering on the previous evening.

On a comparative basis, only small errors (<10%) in sap flow estimatesare produced by large errors (>10%) in K_(g) during high flows. However,at low flows, with the dominance of Q_(r), even small errors in thevalue of K_(g) have the potential to cause large errors in flowestimates. The K_(g) value determined by stem excision at the end of theexperiment (0.782 W/V) was within the range of daily values used.However, the use of the single stem excision K_(g) value for calculatingthe individual daily sap flow estimates substantially altered (3-10x)the accuracy of the gauge estimates on days 1, 2 and 5 and did notimprove gauge accuracy on days 3 and 4. These results suggest that theuse of daily pre-dawn K_(g) values in calculating sap flow is preferableto using a single value of K_(g) determined by stem excision whenworking in a lower range (<50 g h⁻¹) of sap flow rates.

Another important aspect of the gauge's operation is the response ofT_(so) -T_(si). This temperature difference is estimated by the sensorslocated on the stem surface and is assumed to provide an accuratemeasure of the xylem fluid on the same radial plane as the sensors. Whensoil water availability was greatest on days 1, 2 and 5, T_(so) -T_(si)initially increased and then rapidly decreased as flow rates approachedthe diurnal maximums. This response pattern is due to a distortion ofthe isothermal field in the direction of flow. When the largest portionof the heat balance is due to convection, T_(so) -T_(si) becomes themost important component in the computed flow rates, and errors inestimating T_(so) -T_(si) become more probable because of strongtemperature gradients at the outer stem edge. The partial derivative ofeqn 3 with respect to T_(so) -T_(si)

    F/(T.sub.so -T.sub.si)=-Q.sub.f /(c(T.sub.so -T.sub.si).sup.2)(4)

demonstrates that changes in F are proportional to Q_(f) and inverselyproportional to T_(so) -T_(si) Thus, F is especially susceptible toerrors when Q_(f) is large and T_(so) -T_(si) is less than 1.0° C.

Because stem thermal conductivity is a system constant and small stemsizes places limits on heater size, the only alternative in adjustingthe magnitude of T_(so) -T_(si) is by varying Q. Because ofphysiological considerations and errors associated with the magnitude ofgauge signals, however, limits on Q also exist. Proper selection of Qand thus T_(so) -T_(si), becomes important for a particular plant. FIG.9 shows that when Q=0.07 W, the T_(so-T) _(si) versus sap flowrelationship assumed the typical response curve, whereas at lower Q, thecurves lost the characteristic shape even though gauge accuracy (<±5%)among the tests were not different (see also FIG. 7C). Adjustments in Qtypically do not improve gauge performance at high flow rates. However,the relationship between T_(so) -T_(si) and sap flow may provide adiagnostic tool for determining optimum Q under conditions of high soilwater availability.

The physical impact of using Q=0.07 W on the plant was evident by stemsurface temperatures that ranged from 208° C. higher than airtemperatures (Table). With similar diurnal maximum air temperatures overtime, the higher stem surface temperatures on days 3 and 4 apparentlywere related to lower flow rates. Under low flow conditions, heat is nottransported out of the gauge by convection and remains containedwithin-the gauge region by the foam insulation. Although stemtemperatures approached 40° C. for 2 days, physical damage to the stemsurface was much less than expected and apparently did not restrict sapflow on day 5. In addition, at Q=0.07 W for the greenhouse test, T_(so)-T_(si) was maintained above 1° C. As previously mentioned, becauseT_(so) -T_(si) is in the denominator of the flow equation, it becomesimportant to maintain an adequate temperature difference and to preventT_(so) -T_(si) from approaching zero at high flows. UnderestimatingT_(so) -T_(si) during high flows then leads to large overestimates ofsap flow. The problems of stem heating under low flow conditions andpotential errors in calculations at high flows could be addressed bysuing the variable heating methods. The variable heating methodmaintains a constant T_(so) -T_(si) by adjusting Q in response tochanges in F. During low flow on days 3 and 4 in this study, T_(so)-T_(si) was quite steady (2.5-3.0 C) and was not strongly influenced bydiurnal changes in flow. Thus, it is unlikely that a power controllerwould have improved the final results.

Gauge response

Dynamic response of the gauge hereof was evaluated by the time constantmethod (Kucera et al.; Biologia Plantarum, 19:413-420 (1977)) using astep change in a sap flow rate and calculating the time required for thegauge to register a 63% difference. Regression analysis of the responsewas then used to compute the time constant assuming a first order model(Jordan, Instrumentation and Measurement for Environmental Sciences,American Society of Agricultural Engineers, Chap. II (1983)). The stepchange was caused by severing the plant stem immediately above the gaugeduring the high flow period. The plant used for this test was the samefrom which the greenhouse results were obtained. FIGS. 10 and 11 showsthat at a flow rate near 50 g/h, the gauge time constant was 15 s. Thisis much less than the 20 minute time constant reported for small treesand 5-20 minutes for other herbaceous species. The lower response timecan be attributed partly to the small mass of the heated segment (0.26g) and partly to the relatively high flow rate. Even at a flow rate of25 g/h, the small size of the heated stem segment should result,theoretically, in a time constant near 30 s. This rapid response toabrupt changes in flow rate would allow the gauge to be used in suchphysiological applications as stomatal response to atmosphericpollutants, the effects of blue light-stimulated stomatal conductance,or short-term radiation fluctuations within plant canopies.

We claim:
 1. A sap flow gauge comprising:a generally U-shaped bodyhaving a central bight portion and a pair of spaced, opposed legs, saidbight portion presenting a passageway for receiving a plant part, withsaid legs extending generally laterally from the plant part; heatingmeans adjacent said bight and oriented for heating said plant partwithin said passageway; means for sensing radial heat flux andtemperature differential values exhibited by said plant part in responseto heating thereof by the heating means; and filler means disposedbetween said legs and located proximal to said plant part for insuringengagement between said plant part and heating means when said gauge isapplied to said plant part.
 2. The sap flow gauge of claim 1, saidfiller means comprising a pair of filler pads respectively carried byeach of said legs.
 3. The sap flow gauge of claim 1, said radial heatflux sensing means comprising a thermopile carried by said bightadjacent said heating means.
 4. The sap flow gauge of claim 1, saidtemperature differential sensing means comprising a pair of spacedthermocouples supported by said bight.
 5. The sap flow gauge of claim 1,said body being formed of cork-neoprene gasket material.
 6. The sap flowgauge of claim 1, including a jacket of thermal insulation Materialsurrounding said body.
 7. The sap flow gauge of claim 1, including clipmeans for releasably pressing said legs together.